Abstract
AbstractWe study thek-epistasis of a fitness function over a search space. This concept is a natural generalization of that of epistasis, previously considered by Davidor, Suys and Verschoren and Van Hove and Verschoren [Y. Davidor, in:Foundations of genetic algorithms, Vol. 1, (1991), pp. 23–25; D. Suys and A. Verschoren, ‘Proc Int. Conf. on Intelligent Technologies in Human-Related Sciences (ITHURS’96), Vol. II (1996), pp. 251–258; H. Van Hove and A. Verschoren,Comput. Artificial Intell.14(1994), 271–277], for example. We completely characterize fitness functions whosek-epistasis is minimal: these are exactly the functions of orderk. We also obtain an upper bound for thek-epistasis of nonnegative fitness functions.
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